Sunao Katabuchi pulled a book out of his bag and held it up to the audience at a recent screening of his film “In This Corner of the World.” It was ratty, folded and in pieces, because for six years, he took diligent notes and was painstakingly accurate in recreating 1940s Hiroshima before the atomic bomb dropped.

Katabuchi interviewed Japanese survivors kept out of the city, all of whom are now in their eighties. He got a glimpse of how people in Japan lived in the months leading up to...